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3 years ago

The angle bisectors of AXYZ are XG, YG, and ZG. They meet at a single point G.

Mathematics

1 answer:

Harrizon [31]3 years ago

3 0

Answer:

m∠FXD = 36°

EG = 10

m∠FZG = 24°

Step-by-step explanation:

In triangle XYZ, G is the incenter of the triangle.

Since, m∠FXG = 18°

And m∠FXD = 2(m∠FXG)

= 2 × 18°

= 36°

Since, point G is equidistant from all sides (Property of incenter of a triangle)

Therefore, DG = EG = GF = 10

Since, m∠X + m∠Y + m∠Z = 180°

2(m∠FXG) + m∠DYE + 2(m∠FZG) = 180°

2(18)° + 96° + 2(m∠FZG) = 180°

2(m∠FZG) = 180° - 132°

m∠FZG = 24°

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A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. (a) What must be true

valentina_108 [34]

Answer:

(a) The distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b) The value of $P(\bar X$ is 0.7642.

Step-by-step explanation:

A random sample of size n = 10 is selected from a population.

Let the population be made up of the random variable X.

The mean and standard deviation of X are:

$\mu=68\\\sigma=15$

(a)

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. n = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

Then, the mean of the distribution of the sample mean is given by,

$\mu_{\bar x}=\mu=68$

And the standard deviation of the distribution of the sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{10}}=4.74$

Thus, the distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b)

Compute the value of $P(\bar X$ as follows:

$P(\bar X$

$=P(Z$

*Use a z-table for the probability.

Thus, the value of $P(\bar X$ is 0.7642.

(c)

Compute the value of $P(\bar X\geq 69.1)$ as follows:

Apply continuity correction as follows:

$P(\bar X\geq 69.1)=P(\bar X> 69.1+0.5)$

$=P(\bar X>69.6)$

$=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{69.6-68}{4.74})$

$=P(Z>0.34)\\=1-P(Z$

Thus, the value of $P(\bar X\geq 69.1)$ is 0.3670.

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3 years ago

A line passes through (2, 9) and has a zero slope. Write an equation of the line satisfying the given conditions.

zubka84 [21]

Okay so for finding the equation of a line, which is a function, the equation is set to y, so you can eliminate A and B. When the slope of an equation is 0, we are saying that the y value of any point of the line is going to be the same, which is 9 from the given point (2,9).

So the answer is C. y=9

5 0

3 years ago

Montano1993 [528]

Answer:

commutative property

Step-by-step explanation:

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3 years ago

A certain television is advertised as a 53-inch TV (the diagonal length). If the width of

zhenek [66]

The TV is 45 inches tall.

Step-by-step explanation:

The diagonal length of television = 53 inches

Width of TV = 28 inches

As TV is in rectangular or square shape, a diagonal will form a right triangle

Where,

Diagonal = hypotenuse = c = 53 inches

Width = base = b = 28 inches

Length = perpendicular = a

we will use pythagorean theorem to find the length.

$a^2+b^2=c^2\\a^2+(28)^2=(53)^2\\a^2+784=2809\\a^2=2809-784\\a^2=2025$

Taking square root on both sides

$\sqrt{a^2}=\sqrt{2025}\\a=45$

The TV is 45 inches tall.

Keywords: triangle, square root

Learn more about square root at:

#LearnwithBrainly

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3 years ago

Identify the sample chosen for the study. The number of hours a group of 12 children in Mrs. Smith's kindergarten class sleep in

LuckyWell [14K]

Answer:

The 12 children selected in Mrs. Smith's kindergarten class.

Step-by-step explanation:

A sample is a representative part of a population on which a research is carried out.

The study In Mrs Smith's class was to find out the number of hours the children in Kindergarten Sleep in a day. Out of the total number of students, 12 were selected for observation. The 12 childen selected is therefore a sample of the class.

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